"Chapter 1 - The Op Amp's Place in the World" - HTL Wien 10

Low-Pass Filter Design
Example 16–1. First-Order Unity-Gain Low-Pass Filter
16-14
For a first-order unity-gain low-pass filter with f C = 1 kHz and C 1 = 47 nF, R 1 calculates
to:
R1 a1
2fcC1 1
2·103Hz·47·109 3.38 k
F
However, to design the first stage of a third-order unity-gain Bessel low-pass filter, assuming
the same values for f C and C 1, requires a different value for R 1. In this case, obtain
a 1 for a third-order Bessel filter from Table 16–4 in Section 16.9 (Bessel coefficients) to
calculate R 1:
R1 a1
2fcC1 0.756
2·103Hz·47·109 2.56 k
F
When operating at unity gain, the noninverting amplifier reduces to a voltage follower (Figure
16–14), thus inherently providing a superior gain accuracy. In the case of the inverting
amplifier, the accuracy of the unity gain depends on the tolerance of the two resistors, R 1
and R 2.
V IN
R 1
C 1
Figure 16–14. First-Order Noninverting Low-Pass Filter with Unity Gain
16.3.2 Second-Order Low-Pass Filter
There are two topologies for a second-order low-pass filter, the Sallen-Key and the Multiple
Feedback (MFB) topology.
16.3.2.1 Sallen-Key Topology
The general Sallen-Key topology in Figure 16–15 allows for separate gain setting via
A 0 = 1+R 4/R 3. However, the unity-gain topology in Figure 16–16 is usually applied in filter
designs with high gain accuracy, unity gain, and low Qs (Q < 3).
V OUT